A method for assessing the risk of small hydropower outages during typhoon disasters based on a chance-constrained model

Abstract

The present invention discloses a method for assessing the risk of small hydropower outages during typhoon disasters based on a chance-constrained model. The method comprises the following steps: performing Latin hypercube sampling based on the probability distribution function of the predicted output of the small hydropower station; performing Monte Carlo simulation, substituting the sample values ​​into the power system containing the small hydropower station to perform probabilistic power flow calculations; analyzing the small hydropower outage as an independent event, taking into account the uncertain output of the remaining small hydropower stations in the system when calculating the consequences of the small hydropower outage risk, and establishing a chance-constrained optimal load shedding model; converting the chance-constrained optimal load shedding model into a deterministic equivalent model and solving it using CPLEX; and multiplying the probability of small hydropower station outage by the minimum load shedding cost of the power system containing the small hydropower station to obtain a small hydropower station outage risk value. The present invention effectively addresses the conflict between the incompatibility between power grid security and economic efficiency caused by small hydropower station outages and can be used to assess the risk of small hydropower station outages during typhoon disasters.

Description

Technical Field

[0001] The present invention belongs to the technical field of power distribution networks, and in particular relates to a method for assessing the risk of small hydropower outages under typhoon disasters based on a chance constraint model. Background Art

[0002] Small hydropower refers to hydroelectric stations or hydroelectric generating facilities with very small installed capacity. There is no consistent definition of small hydropower or capacity ranges defined globally. For example, my country currently stipulates that the average installed capacity of small hydropower is less than 50MW.

[0003] Small hydropower stations, as a distributed clean energy source with mature technology and high economic efficiency, have great development potential. However, most small hydropower stations are run-of-river stations. Their output fluctuates with changes in river flow and precipitation, resulting in uncertainty and weak controllability. Furthermore, small hydropower stations are typically located in remote areas far from load centers, with limited local load demand. Most are connected at the end of branch lines in the distribution network. Once connected, small hydropower stations complicate tidal flow patterns, increasing their randomness. During the annual typhoon season, heavy rains brought by typhoons often lead to severe flooding. Typhoons significantly increase the inflow to small hydropower stations, increasing their output. This increases the stability of the power grid and the small hydropower stations themselves, posing a significant threat to the stability of the power grid. This can cause voltage violations at power system nodes and overloads on branch lines. It can also squeeze limited transmission channels, impacting the output of other power stations. To ensure the safe and stable operation of the power system and mitigate risks, it is necessary to adjust the output of hydropower units or force them to shut down. However, many run-of-river small hydropower stations cannot regulate their output, so they are often shut down when their output is excessive to maintain stable and safe power system operation. Typhoon-induced shutdowns of small hydropower stations pose risks to the safe and stable operation of the power system. Therefore, it is necessary to study methods for assessing the risk of small hydropower shutdowns during typhoon disasters. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for assessing the risk of small hydropower outages under typhoon disasters based on a chance constraint model, which can be used to assess the risk caused by the outage of each small hydropower station under typhoon disasters.

[0005] To achieve the above object, the present invention is implemented by adopting the following technical solution: a method for assessing the risk of small hydropower outage under typhoon disasters based on a chance constraint model, comprising the following steps:

[0006] Step 1: Perform Latin hypercube sampling based on the probability distribution function of the predicted output of the small hydropower station to generate sample values;

[0007] Step 2: Combined with the system operation plan, Monte Carlo simulation method is used to perform probabilistic power flow calculation to obtain the voltage over-limit probability of the small hydropower access node, that is, the outage probability;

[0008] Step 3: Considering the uncertainty of the output of the remaining small hydropower stations in the distribution network, an optimal load shedding model based on chance constraints is established, and the system load shedding penalty term is included in the objective function;

[0009] Step 4: Use the probability distribution of the small hydropower output to perform an opportunity constraint equivalent transformation, convert it into a model that can be solved by CPLEX, and then solve it;

[0010] Step 5: Multiply the outage probability of the small hydropower station by the minimum generator and load shedding cost of the power system including the small hydropower station to obtain an outage risk value of the small hydropower station.

[0011] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method for assessing the risk of small hydropower outages under typhoon disasters based on a chance constraint model is implemented.

[0012] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned method for assessing the risk of small hydropower outage under typhoon disasters based on a chance constraint model.

[0013] Compared with the existing technology, the beneficial effects of the present invention are: the present invention takes into account the probability of small hydropower station shutdown under typhoon disasters, and takes the minimum load shedding cost after the small hydropower station shutdown as the risk consequence, effectively dealing with the contradiction between the safety and economy of the power grid caused by the shutdown of small hydropower stations. It can be used to evaluate the risks caused by the shutdown of small hydropower stations during typhoon disasters, and provide a reference for typhoon disaster prevention such as the allocation of emergency materials and rapid repairs after failures. It has certain theoretical and engineering value. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of the method for assessing the risk of run-of-river small hydropower outage under typhoon disasters based on the chance-constrained optimal load shedding model of the present invention.

[0015] Figure 2 This is a load node voltage probability distribution diagram provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0016] like Figure 1 As shown, the present invention provides a method for assessing the risk of run-of-river hydropower station shutdown under typhoon disasters based on a chance-constrained optimal load shedding model, the method comprising the following steps:

[0017] Step 1: Perform Latin hypercube sampling based on the probability distribution function of the predicted output of the small hydropower station to eliminate the correlation between samples and generate sample values;

[0018] Step 2: Monte Carlo simulation is used to calculate the probabilistic power flow based on the sampled values, and the voltage over-limit probability of the small hydropower access node is used as the small hydropower outage probability;

[0019] Step 3: Establish a chance-constrained optimal load shedding model that takes into account the generator shedding penalty term and transform it into a deterministic equivalent model that can be directly solved using CPLEX to obtain the risk consequences of small hydropower outages.

[0020] Step 4: Multiply the outage probability of the small hydropower station by the optimal generator and load shedding cost of the system after the outage of the small hydropower station to obtain the outage risk value of the small hydropower station.

[0021] Step 1: Use the Latin hypercube sampling method based on the probability distribution of small hydropower output prediction, as follows:

[0022] Step 1-1: divide the value range [0, 1] of the probability distribution function of the predicted output of the small hydropower station into U non-overlapping areas, randomly select a random number in each area and obtain U sample values ​​after inverse transformation.

[0023] x u =F -1 (r u / U+(u-1) / U)

[0024] Among them, F -1 (·) is the inverse function of the probability distribution of the predicted output of the small hydropower station; u is the region number; U is the number of regions divided by the probability distribution function; r u represents the random number taken in the uth interval; x u Indicates the u-th sample value obtained by sampling.

[0025] Step 1-2, randomly generate the initial order matrix Each row is from 1 to N s The sampling matrix X is composed of random permutations. c Each row of elements is sorted according to the initial order matrix.

[0026] Steps 1-3, calculate the correlation coefficient matrix ρ of the initial order matrix L , and perform Cholesky decomposition

[0027] ρ L =DD T

[0028] Where: D is the lower triangular matrix.

[0029] Steps 1-4, calculate the matrix based on the lower triangular matrix D It can be obtained by the following formula

[0030] G=D -1 L

[0031] At this time, the correlation coefficient matrix of G is the identity matrix.

[0032] Steps 1-5: Update the elements of each row of the sequential matrix L according to the size order of the elements of each row of the G matrix, and update the sampling matrix X c Each row of the updated sequence matrix L is rearranged to obtain a sample matrix X with smaller correlation s .

[0033] Step 2: Monte Carlo method is used to perform probabilistic power flow calculation. The probability of small hydropower outage is obtained based on the voltage over-limit probability of the small hydropower access node, as follows:

[0034] The S sample values ​​are substituted into the distribution network system one by one for deterministic power flow calculation. The voltage of each load node is calculated using Mat-Power, and the Gaussian kernel function is selected as the kernel function of non-parametric kernel density estimation. The node voltage calculation value is fitted using the non-parametric kernel density estimation method to obtain the probability distribution of the load node voltage. A voltage amplitude threshold of the small hydropower node is set. When the small hydropower node voltage exceeds the threshold, it will be shut down. The probability of the small hydropower node voltage crossing the threshold is used as the shutdown probability of the small hydropower station.

[0035] Step 3: Establish an opportunity-constrained optimal load shedding model that takes into account the generator shedding penalty term, and use the generator shedding and load shedding costs as the risk consequences of each small hydropower outage:

[0036] Step 3-1: Establish the objective function of the opportunity-constrained optimal load shedding model taking into account the generator shedding penalty term:

[0037]

[0038] Where: N represents the number of system load nodes; is the decision variable of the model, which represents the active load removed at node i at time t; u t =[u 1，t ,u 2，t ,…,u N，t ] T represents the small hydropower operation state vector at time t, u i，t =0 means that the small hydropower station at node i is cut off at time t or the node does not contain small hydropower station, u i，t =1, indicating that the small hydropower station at node i at time t is in operation; I = [I1, I2, ..., I N ] Tis the initial state vector of the small hydropower station, is a given known vector of the system, if there is no small hydropower at node i or the small hydropower has been shut down, then I i = 0, if there is a small hydropower station at node i, then I i =1; M is a pre-set large value. When the small hydropower station at node i is shut down, the load shedding amount is added as a penalty term, indicating an increase in the active control cost.

[0039] Step 3-2, add constraints to the opportunity-constrained optimal load shedding model:

[0040] Load node voltage amplitude constraint:

[0041]

[0042]

[0043] Where: V i Represents the square of the node voltage amplitude; V i，max and V i，min They represent the upper and lower limits of the square of the node voltage amplitude respectively; Pr(·) represents the probability that the constraint condition is met, and α is a preset confidence level, such as 5%.

[0044] Node load shedding constraints:

[0045]

[0046] Where, represents the node load shedding amount at node i at time t; It represents the total load at node i at time t. The present invention sets the maximum allowable load removal amount of the node as the total load of the node.

[0047] The linearized power flow calculation equation of the distribution network is:

[0048] V t =RP t +XQ t +v01 N

[0049] R=2(A T diag -1 (r)A) -1

[0050] X=2(ATdiag -1 (x)A) -1

[0051]

[0052]

[0053] Where V t represents the square vector of voltage amplitude at each node of the distribution network at time t; P t represents the active power injection vector of each node at time t, P t The active power output vector of the small hydropower plants running in the system Node load vector P t L and the load shear vector P t C Composition; Q t represents the active power injection vector of each node at time t. From formula (2.33), we can know that Q t The reactive power output vector of the small hydropower plants running in the system Node reactive load vector where v0 represents the square of the voltage amplitude of the root node of the distribution network, and A represents the node association matrix of the distribution network system.

[0054] Step 3-3, convert the chance constraint model into a deterministic equivalent model that can be solved using CPLEX:

[0055] The shutdown of each small hydropower station is analyzed as an independent event. It is assumed that the predicted output of small hydropower stations is independent of each other and obeys the normal distribution. Based on the assumption of the probability distribution of the predicted output of small hydropower stations and the linearized distribution network voltage calculation, the chance constraint can be converted into a deterministic equivalent model.

[0056]

[0057]

[0058] Where: K α , K 1-α represents the quantile of the random variable, V0 represents the square of the voltage amplitude at the root node of the distribution network, R i represents the i-th row of matrix R, X i Represents the i-th row of the X matrix.

[0059] Steps 3-4 are solved using CPLEX:

[0060] First, we use enumeration to list all possible combinations of small hydropower units, i.e., all possible generator tripping scenarios. After determining each possible generator tripping scenario, we combine the predicted small hydropower output probability distribution to solve for the quantiles of the random variable, thus converting the problem into one that can be solved directly using CPLEX.

[0061] Step 4: Multiply the outage probability of the small hydropower station by the optimal system load shedding cost after the small hydropower station is shut down to obtain the outage risk value of the small hydropower station. The formula is as follows:

[0062]

[0063] The method provided in the embodiment of the present invention starts from the static safety constraints of the distribution network, considers the possibility of small hydropower station shutdown during typhoon disasters, and takes the minimum cost of distribution network load shedding after the small hydropower station shutdown as the risk consequence. It effectively addresses the contradiction between safety and economy, can assess the risks caused by the shutdown of small hydropower stations during typhoon disasters, and can provide a reference for typhoon disaster prevention such as the allocation of emergency repair materials and rapid repair after failures. It has certain theoretical and engineering value.

[0064] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0065] Example

[0066] This embodiment of the present invention uses an adjusted IEEE 33-node system containing small hydropower stations for example analysis. In this example, the system is connected to four small hydropower stations: A, B, C, and D, connected to nodes 18, 22, 25, and 33, respectively, with an access capacity of 8 MW each. This embodiment assesses the operational risks of each of these four small hydropower stations. This system uses node 0 as the balancing node, with a voltage amplitude set to 1.0 (pu). The voltage amplitude upper limit for each of the remaining nodes is 1.05 (pu), and the node voltage amplitude lower limit is 0.90 (pu). The threshold for the small hydropower access node exceeding the threshold is set to 1.1 (pu). If the voltage amplitude of a small hydropower access node exceeds this threshold, the small hydropower station is shut down.

[0067] When performing probabilistic power flow calculations, small run-of-river hydropower units are considered PQ nodes, and the power factor is set to 0.8. The predicted output of small hydropower stations follows a normal distribution, with the expected value being the deterministic predicted power value, and the standard deviation being 10% of the expected value. The predicted output of small hydropower stations is used as the input for the risk assessment method of this embodiment. Assuming that the expected value of its output at a certain moment under a typhoon disaster is as shown in Table 1 below.

[0068] Table 1 Predicted output of small hydropower stations

[0069] Small hydropower stations Forecast output (MW) A 6 B 5 C 4 D 6

[0070] Combined with the probability distribution of each small hydropower station output, the LHS-cd method is used to sample the output of each small hydropower station, the sampling number is 30,000 times, and the Monte Carlo method is used to calculate the probability flow. The probability distribution of the voltage at the access node of each small hydropower station is as follows: Figure 2 shown.

[0071] This example considers each small hydropower outage as an independent event and does not consider the possibility of a combined outage. After determining the voltage over-limit probability at each small hydropower station's access node using probabilistic power flow, this over-limit probability is used as the outage probability for each small hydropower station. The results are shown in Table 2.

[0072] Table 2 Probability of small hydropower outage

[0073] Small hydropower stations Outage probability A 0.2660 B 0.0000 C 0.0000 D 0.0014

[0074] When a small hydropower outage occurs, a certain amount of load must be removed to address potential power shortages in the system. However, due to the uncertainty of the output of other small hydropower plants in the system, relying solely on load shedding may still result in safety constraints not being met within a certain confidence level. Therefore, small hydropower generator shedding is incorporated into the load shedding model as a control measure, and the load shedding amount, taking into account the generator shedding penalty, is used as the control cost in the risk consequence calculation. The generator shedding penalty M is set to 100 in this example. The load shedding amounts and generator shedding schemes corresponding to different small hydropower outage events are shown in Tables 3 and 4.

[0075] Table 3 Load shedding scheme

[0076]

[0077]

[0078] Table 4 Cutting machine plan

[0079]

[0080] In Table 4, 1 indicates that a small hydropower station is operating, and 0 indicates that a small hydropower station is shut down. As can be seen from the table, for the shutdown of small hydropower station A, only load shedding is required to meet the system's safety constraints at a certain confidence level, resulting in a relatively low active control cost. For the shutdown of small hydropower stations B, C, and D, the other small hydropower stations must be shut down without load shedding, resulting in a relatively high active control cost.

[0081] The risk indicators of small hydropower station shutdown under typhoon disasters are shown in Table 5.

[0082] Table 5 Risk values ​​of run-of-river small hydropower outage under typhoon disasters

[0083] Small hydropower number Outage probability Risk consequences Value at Risk A 0.2680 2.4910 0.6676 B 0.0000 0.0000 0.0000 C 0.0000 0.0000 0.0000 D 0.0014 100.0000 0.1400

Claims

1. A method for assessing the risk of small hydropower outages under typhoon disasters based on a chance constraint model, characterized in that: The steps include: Step 1: Perform Latin hypercube sampling based on the probability distribution function of the predicted output of the small hydropower station to generate sample values; Step 2: Combined with the system operation plan, Monte Carlo simulation method is used to perform probabilistic power flow calculation to obtain the voltage over-limit probability of the small hydropower access node, that is, the outage probability; Step 3: Considering the uncertainty of the output of the remaining small hydropower stations in the distribution network, an optimal load shedding model based on chance constraints is established, and the system load shedding penalty term is included in the objective function; The optimization objective is to minimize the load shedding required by the system after the small hydropower plant is shut down. Due to the uncertain output of other small hydropower stations, relying solely on load shedding may not be able to meet the system safety constraints. In this case, small hydropower generator shedding is used as a control measure to ensure that the voltage constraint is met. The objective function of the load shedding opportunity constraint model taking into account the generator shedding penalty term is as follows: Where: N represents the number of system load nodes; is the decision variable of the model, which represents the active load removed at node i at time t; u t =[u 1,t ,u 2,t ,…,u N,t ] T represents the small hydropower operation state vector at time t, u i,t =0 means that the small hydropower station at node i is cut off at time t or the node does not contain small hydropower station, u i,t =1, it means that the small hydropower station at node i at time t is in operation; I = [I1, I2, ..., I N ] T is the initial state vector of the small hydropower station, is a given known vector of the system, if there is no small hydropower at node i or the small hydropower has been shut down, then I i = 0, if there is a small hydropower station at node i, then I i =1; M is a pre-set large value. When the small hydropower station at node i is shut down, the load shedding amount is added as a penalty term, indicating an increase in the active control cost; The load shedding of the distribution network must meet the following constraints: Load node voltage amplitude constraint: Pr(V i,t ≤V i,max )≥1-α Pr(V i,t ≥V i,min )≥1-α Where: V i,t Represents the square of the node voltage amplitude at time t; V i,max and V i,min They represent the upper and lower limits of the square of the node voltage amplitude respectively; Pr(·) represents the probability that the constraint condition is satisfied, and α is the pre-set confidence level; Node load shedding constraints: Where, represents the node load shedding amount at node i at time t; represents the total load at node i at time t, and the maximum allowable load removal of the node is set to the total load of the node; The linearized power flow calculation equation of the distribution network is: V t =RP t +XQ t +v01 N R=2(A T diag -1 (r)A) -1 X=2(A T diag -1 (x)A) -1 Where V t represents the square vector of voltage amplitude at each node of the distribution network at time t; P t represents the active power injection vector of each node at time t, P t The active power output vector of the small hydropower plants running in the system Nodal load vector and the load shedding vector Composition; Q t represents the active power injection vector of each node at time t, Q t The reactive power output vector of the small hydropower plants running in the system Node reactive load vector Composition, v0 represents the square of the voltage amplitude of the root node of the distribution network, A represents the node correlation matrix of the distribution network system; Step 4: Use the probability distribution of the small hydropower output to perform an opportunity constraint equivalent transformation, convert it into a model that can be solved by CPLEX, and then solve it; Convert the chance constraint model into a chance constraint equivalent model that can be solved directly using CPLEX: The shutdown of each small hydropower station is analyzed as an independent event. It is assumed that the predicted output of small hydropower stations is independent of each other and obeys the normal distribution. Based on the assumption of the probability distribution of the predicted output of small hydropower stations and the linearized distribution network voltage calculation, the chance constraint can be converted into a deterministic equivalent model. Where: K α ,K 1-α represents the α quantile of the random variable, V0 represents the square of the voltage amplitude of the root node of the distribution network, R i represents the i-th row of matrix R, X i represents the i-th row of the X matrix; Step 5: Multiply the outage probability of the small hydropower station by the minimum generator and load shedding cost of the power system including the small hydropower station to obtain an outage risk value of the small hydropower station.

2. The method for assessing the risk of small hydropower outage under typhoon disasters based on a chance constraint model according to claim 1 is characterized in that: The calculation methods for the outage probability of small hydropower stations include: The Monte Carlo simulation method is used to calculate the power flow based on the S sampling values ​​of the predicted small hydropower output. The calculated node voltage amplitude is fitted using the non-parametric kernel density estimation method to obtain the voltage over-limit probability of the small hydropower access node and use it as the small hydropower outage probability.

3. The method for assessing the risk of small hydropower outage under typhoon disasters based on a chance constraint model according to claim 1 is characterized in that: Model solving method: First, an enumeration method is used to list all possible combinations of small hydropower units, that is, all the generator tripping schemes. After determining each generator tripping scheme, the quantiles of the random variable are solved based on the predicted output probability distribution of the small hydropower units, thereby converting the problem into a problem that can be directly solved using CPLEX.

4. The method for assessing the risk of small hydropower outage under typhoon disasters based on a chance constraint model according to claim 1 is characterized in that: Calculation of the risk of shutdown of run-of-river hydropower stations under typhoon disasters; According to the shutdown probability of small hydropower station i at time t And the system's load shedding capacity C after the small hydropower station is shut down f After that, the risk value R of small hydropower station i is:

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for assessing the risk of small hydropower outage under typhoon disasters based on a chance constraint model as described in any one of claims 1 to 4 is implemented.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method for assessing the risk of small hydropower outage under typhoon disasters based on a chance constraint model as described in any one of claims 1 to 4 is implemented.

Images